OFFSET
0,1
COMMENTS
REFERENCES
Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187.
LINKS
EXAMPLE
As a triangle:
2,
-1, 1,
-1, -8, -1,
1, 4, -4, -1,
-1, 4, 8, 4, -1,
etc.
MAPLE
DifferenceTableBernoulli := proc(n) local A, m, k; A := array(0..n, 0..n);
# pritty print
for m from 0 to n do for k from 0 to n do A[m, k] := '~' od od;
# compute elements
for m from 0 to n do A[m, 0] := bernoulli(m, 1);
for k from m-1 by -1 to 0 do
A[k, m-k] := A[k+1, m-k-1] - A[k, m-k-1] od od;
convert(A, matrix) end:
A := DifferenceTableBernoulli(13); L := NULL;
for n from 0 to 9 do for k from 0 to n do
L := L, numer(A[3+k, 3+n-k]) od od;
L; # Peter Luschny, Apr 12 2014
MATHEMATICA
max = 13; tb = Table[BernoulliB[n], {n, 0, max}]; td = Table[Differences[tb, n][[3 ;; -1]], {n, 2, max - 1}]; Table[td[[n - k + 1, k]] // Numerator, {n, 1, max - 3}, {k, 1, n}] // Flatten (* Jean-François Alcover, Apr 11 2014 *)
CROSSREFS
KEYWORD
AUTHOR
Paul Curtz, Apr 08 2014
EXTENSIONS
a(9) corrected by Wesley Ivan Hurt, Apr 08 2014
a(4) corrected by Jean-François Alcover, Apr 11 2014
STATUS
approved